I know there is an function that will give you the force at which an
object hits the ground if dropped. For example: a 400 pound object
dropped from a three foot height hits the ground with how much force
in PSI?

Thanks
'

---

Request for Question Clarification by bio-ga on 20 Feb 2003 11:33 PST

PSI is the unit for pressure, not force. To calculate pressure, we
need to know the area, too. Did you mean lbf (pound-force) instead of
psi by any chance?

---

Clarification of Question by scoobydooaz-ga on 20 Feb 2003 14:40 PST

Yes I did mean lbf instead of psi. I want to know how many pounds of
force is exerted on a dropped object.

Gravitational Potential Energy = height * mass * acceleration due to
gravity

example a 3kg which is 4 metres off the ground
PE = 3 * 4 * 9.8
   = 117.6 joules

If that object is dropped then just before it hits the ground all the
potential energy is converted into kinetic energy.
Kinetic energy = 1/2 * mass * velocity^2

So to contiue the above example to find the impact velocity
117.6 = 1/2 * 3 * v^2
v= sqrt(117.6 * 2 /3)
 = 8.85 metres/second

You can calculate the impulse of the collision between the object the
earth.    Asumming the mass of the opbject is constant.

The equation is Impulse = mass * change in velocity
SO for the example
Impluse = 3 * (8.85 - 0)
        = 26.55 Newton seconds

The only way to calculate the force is if you know the duration of the
impact.
Average force = Impluse / Duration of Impact

For instance to continue the example if the impact lasted 1/100 of a
second.
Average force = 26.55 / (1 / 100)
              = 2655 Newtons

Dear Scoobydooaz,

As Popsracer says, there is no single answer to this question.  In
practice, the force between the object and the ground will vary with
time, even in a particular case.  When the object first touches the
ground, there will be a small force.  This force on the object
accelerates it upwards - in other words, slows it down.  But since it
is still moving, both the object and the ground will deform somewhat. 
As they do, of course, the force between the object and the ground
increases, so the acceleration (the rate of loss of speed) does so
too.  At some point the force reaches a maximum, after which it
decreases again as the object relaxes or possibly bounces.  The
precise details of this depend on the detail of the shape and
mechanical properties of the object and the ground.

As Popsracer also says, you can predict the impulse of the collision
from your data: this is the integral of the contact force with respect
to time.  But whether this occurs as a small force over a long period
(as for soft materials) or a larger force for a shorter period (as for
harder materials) cannot be predicted unless we know more about the
problem.  And in either case, the force will not be constant during
this period but will vary during the time the object is in contact
with the ground but has not yet come to rest.

I trust this helps.

Carnegie

Sorry People this is an easy question.  You just have to remember what
is "Force".  Force equals Mass times Acceleration.

The answer is the Force is 400 POUNDS.

This is the English measurement unit system
The units of Force are "pounds"
The units of Mass are "slugs"
The units of Acceleration are "feet/seconds^2"

Therefore a ball of X slugs with an acceleration [Gravity] equals
pounds.

We already know the Force (400 pounds).  This was given by the
question.  The ball has a Mass of 12.43239883 slugs and Gravity is a
constant at sea level (while almost a constant) [32.174 ft/sec^2]

Put them into the equation F=MA
The answer is 400 POUNDS.  Very Easy.  Remember High School Physics. 
It is easy once you use the correct equation and use the correct
units.

Socal, you are correct in that a 400 pound object will experience a
force of 400 pounds due to the earth's gravity.

When the object is falling there is no force to oppose this so the
object accelerates.  When an object is sitting on the ground an equal
an opposing force is cancelling out the effect of grativy so the
object does not accelerate.

However what the original case was asking is if the the force due to
the impact.  You see the object is travelling at a particular speed
down towards the ground.  When hits it has to suddenly shange speed. 
Going back to f = m a.  A force must be exterted to accererate (change
the speed of) the object.

Perhaps it is clear if you consider a case where gravity is taken out
of the question.  If a hockey puck is traveling on the ice towards the
goalie at a particular speed then the goalie must exert a force on the
puck to stop its motion.

Getting back to the original question it is hard to know how the force
is applied over time.  As Carnegie pointed out you can work out the
average force applied over a particular time, but the force will
almost always not be constant.

You have to know <i>Duration of Impact</i>